Transformer ratio based on known induction of coils

[gkmaia]

Is it possible to calculate the expected secondary voltage of a mains transformer (60hz) by knowing it's primary voltage, primary coil induction and secondary coil induction?

[TimFox]

For a perfect transformer, with negligible leakage inductance and a linear magnetic path, the voltage (turns) ratio should scale as the square root of the inductances.
However, in a practical transformer, the magnetic material's permeability will be a nonlinear function of the flux density in the iron, starting from a relatively low value at zero, reaching a maximum value partway up the magnetization curve, flattening above the maximum slope, and then dropping quickly at saturation flux density.
Therefore, the ratio of inductances may vary with the applied test voltage when you measure the two inductances.  The applied voltage from your test system is probably much lower than the AC voltage applied under normal operation.

[T3sl4co1l]

This.  If you could adjust the excitation so it's the same frequency, and volts per turn, you can expect the same inductance.  But then your problem would already be solved...

Also, edge cases: transformers with shunts have some lower coupling factor between primary and secondary/ies, so you won't get an integer turns ratio.  Only two common cases of these: microwave oven transformers and other current limited supplies (old AC welders, neon sign transformers), and ferroresonant transformers (where the output voltage is set by line frequency).

Tim

[CatalinaWOW]

Good answers.  Your question is also a fairly subtle way to evaluate people.

Those with only theoretical knowledge of the circuit will answer yes and pop out a set of equations.  The answers given reflect the truism that the model is not reality, and in magnetics that truism is more likely to apply than in many other areas.  It is possible to model this pretty well, but it requires far more information than you provided (and more than is usually readily available).

Another way to think about this is an apparently minor rephrase of the question.  "Is it possible to correctly calculate...".

Through a basic degree, grad school and decades of on the job and in the hobby lab learning I have learned a lot.  Each year increases my store of knowledge.  And finds me saying "I don't know." or "It depends."  more and more often.

[T3sl4co1l]

Or judging the depth and subtlety of ones' models.  For example, I know all of these things (transformer design, bulk core properties), but I can't tell you why they happen.  I'd love to rattle off the equations, if there were any.   This is ultimately rooted in the incredible complexity of condensed matter physics, where even tiny impurities, vacancies, dislocations, defects in the magnetic crystal can have profound, unpredictable effects on its macroscopic properties.

It's an empirical model.  We note (but arguably not really understand) parameters like initial and average permeability, saturation, core loss and so on.  For which, you merely need to perform dozens or hundreds of measurements, then fit curves, and there are your parameters.  For that one core, in that size, in that condition...

A more basic theoretical model is in principle possible, but no closed-form solution is possible (that would produce our empirical parameters from physical inputs), and no approximate solution is known.  And so we also come to the economy of theory itself: it would require decades of intensive work to derive such solutions, but the economic value in those solutions is minuscule, so no one will solve them.  At least until such time as that effort can clearly be amortized over a large enough time period, or divided into small enough pieces, or -- in my opinion more likely -- solved as a side-effect of some more important condensed-matter physics problem (say, nanotechnology for various purposes: computation, data storage, chemical processing, bioengineering, etc.).

The applied outcome of this, to this thread, would be: if you knew the core material and its exact condition, you could in principle know its nonlinear parameters, and perhaps not by measuring a single point on each winding, but several excitation values for each, or at different frequencies, or even waveforms say -- you would be able to match them up, and determine the winding ratio with good confidence.  But clearly this is much more difficult than, say, even x-raying the transformer to count its turns directly -- so "basically no" is a good answer.

Tim